What should a person do if their ablution is invalidated while performing prayer in congregation?

If a person’s ablution is invalidated while performing prayer in congregation, they should either perform ablution again and repeat their prayer—which is the more virtuous option—or, without doing anything else that would further invalidate the prayer, quietly leave, perform ablution, and return to continue their prayer from where they left off with the imam. If the imam has finished the prayer by the time they return, they should wait for about as long as the imam would have waited, without reciting anything as if they were still following the imam, and complete their prayer by reciting only the tasbihs in bowing and prostration, and the supplications and salawat in the sitting position. (Merghinani, al-Hidaya, 1/59-61; Ibn Abidin, Radd al-Muhtar, 1/612 ff.)

If a person in the front row of a crowded mosque has their ablution invalidated while performing prayer in congregation, and if according to some schools of thought their ablution would not be considered invalid, they may follow that school and continue their prayer. For example, a Hanafi whose wound is bleeding may complete their prayer by following the Shafi‘i or other schools that do not consider bleeding to invalidate ablution. However, if something occurs that all jurists agree invalidates ablution—such as urination or passing gas—and it is not possible to reach the place for ablution due to the crowd, the person should sit and wait for the prayer to finish, or act as if nothing happened so as not to distract other worshippers. Afterwards, they should perform ablution and repeat their prayer.

Source: T.C. Diyanet İşleri Başkanlığı, Din İşleri Yüksek Kurulu